Code for ``Identifying The Latent Space Geometry Of Network Formation Models Via Analysis Of Curvature."

This code implements the geometry classification methods from Identifying Latent Space Geometry in Network Models using Analysis of Curvature by Lubold et al (https://arxiv.org/abs/2012.10559). Send questions or comments to Shane Lubold at sl223@uw.edu. The Indian Villages data used in this paper is not available publicly, so we only provide the code to reproduce the C Elegans example.

Files:

• Bootstrap.py: Implements the bootstrapping method used to test the three geometry hypotheses (Euclidean, spherical, and hyperbolic).
• celegans131matrix.csv: Contains the adjacency matrix of a neuron network in a C. Elegans worm. This data can be accessed here: https://www.dynamic-connectome.org/?page_id=25
• Classification_CElegans_Repeat.py: Classifies the C Elegans neural network available in celegans131matrix.csv.
• Compute_Rate.py: Implements an estimator of the rate of the sequence \tau_n that appears in Section 2 of https://projecteuclid.org/euclid.aos/1176325770. Currently, our method does not use this code. We simply use \tau_n = 1/3. However, future work could use this code to construct use better rate estimates.
• Generate_Hyperbolic.py: Simulates positions and distances on hyperbolic space.
• Make_D_Spherical.py: Simulates positions and distances on spherical space.
• Make_Euclidean_D.py: Simulates positions and distances on Euclidean space.
• Rank_Estimator.py: Estimates the rank of a matrix from a noisy estimate of the matrix. We implement the "ladle" estimator from https://academic.oup.com/biomet/article-abstract/103/4/875/2659039.
• Supplementary_Files.py: Contains various pieces of code that we need, such as estimating the distance matrix from the adjacency matrix.
• Type1_Power.py: Computes the type 1 and error for the geometry classifier.
• Estimate_Curvature.py: Estimates the curvature of the latent space from a matrix of distances between points in the latent space.